Computational Aerodynamics. ANSLab specializes in developing techniques for numerical solution of problems in aerodynamic. In particular, we are working to take advantage of both the geometric flexibility of unstructured mesh methods and the accuracy benefits of high-order methods. We apply these techniques to compressible aerodynamics problems. We have demonstrated that high-order methods can achieve solutions of engineering accuracy more quickly than second-order methods. Current work is focused on extending these results to complex 3D turbulent viscous flows.

Unstructured Mesh Generation. Hand-in-hand with research in unstructured mesh flow solvers, we also study unstructured mesh generation, which is the process of decomposing a domain into cells or elements. We have an extensive history in generation of provable-quality triangular (2D) and tetrahedral (3D) meshes. We have also developed techniques for anisotropic mesh adaptation that produce alignment of the mesh with the gradients in the solution, improving accuracy and efficiency of the flow solver. Recently, we have developed a new technique for anisotropic mesh generation that produces predominantly quadrilateral (2D) and prismatic (3D) meshes throughout the domain. Our meshing work is contained in a software library that is freely available for non-profit use.

Error Assessment and Control for Unstructured Mesh Methods. The ultimate goal of CFD simulations is to provide an answer that is not just accurate, but which has known error bounds.  Assessment of error in output quantities like lift and drag is well established for finite element methods, but these methods are less commonly used for finite volume methods, perhaps because of the poor behavior of some measures of error.  We are working to improve understanding of error for unstructured mesh finite volume methods and to exploit that understanding to provide good error bounds on output quantities. At the same time, we are working to identify mesh features that are particularly harmful for accuracy and use that knowledge to generate better meshes.

Stability and Convergence for Unstructured-Mesh Finite-Volume Methods. Fairly often, an aerodynamics simulation doesn’t converge properly to steady-state, even though the physical flow should be steady. Sometimes, this takes the form of the solution “blowing up” — growing without bounds in ways that are clearly unphysical.  Other times, the solution does eventually reach steady state, but does this very slowly. We have developed methods to address both of these problems, using a combination of modal analysis, machine learning, and mesh improvement techniques. Currently, we are working to understand and remediate cases that lead to a limit cycle, where the solution oscillates without converging to steady state, for reasons strictly related to numerics.